Instead of studying galaxies as discrete objects residing in dark matter halos, one can track the cosmological quantities that comprise the baryon budget. Galaxy formation and evolution plays the fundamental role in the processing of baryons from neutral hydrogen to molecular gas to stars to metals. Star formation is inextricably linked with galaxy formation; whether you choose to define a galaxy as a large conglomeration of stars or an overdensity of baryons inside a collapsed dark matter halo, the galaxies in our universe form great numbers of stars. The cosmological quantities of interest provide integral constraints on star formation. The cosmic star formation rate density (SFRD) is an integral constraint averaged over the volume of the universe observable at a given redshift. The cosmic density of neutral gas, gas, the cosmic density of metals, Z, and the cosmic stellar mass density all provide integral constraints on the SFRD over time, as will be discussed below. The sum of the cosmic infrared background (CIB) and cosmic far-infrared background (FIRB) radiation provides an integral constraint on the SFRD from the Big Bang all the way to z = 0 by tracing the energy generated by nuclear reactions in stars.
2.1. Cosmic Density of Neutral Gas
The Damped Lyman Absorption systems (DLAs, Wolfe et al. 1986) are quasar absorption line systems with HI column densities 2 × 1020 cm-2, sufficient to self-shield against the high-redshift ionizing background. Studying quasar absorption-line spectra provides a (nearly) unbiased sample of lines-of-sight through the cosmos ideal for measuring cosmological quantities. The DLAs have been found to contain the majority of neutral hydrogen atoms at high redshift (see the recent review by Wolfe, Gawiser & Prochaska 2005). Moreover, DLAs contain the vast majority of neutral gas, by which we mean neutral hydrogen and helium in regions that are sufficiently neutral to cool and participate in star formation, as lower column density systems are predominantly ionized. Hence the DLAs provide the reservoir of neutral gas that is available for star formation. In a simple closed box model, dgas / dt = - d / dt, and the net decrease in the cosmic density of neutral gas from z = 3 to z = 0 is assumed to have all been turned into stars (see Fig. 5 of Wolfe et al. 2005). In that case, the DLAs appear to have formed about half of the stars seen in galaxies today. The truth is more complicated in hierarchical cosmology, where an open box model must be used;
Cosmological models for infall of gas from the intergalactic medium (IGM), merging of lower column-density systems, and gas loss due to galactic winds are still quite uncertain, but the star formation rates actually measured for DLAs (Wolfe, Gawiser, & Prochaska 2003a; Wolfe, Prochaska, & Gawiser 2003b, Wolfe et al. 2004) imply that DLAs could have formed all present-day stars. Unfortunately, large uncertainties in the source and sink terms prevent us from using changes in the cosmic density of neutral gas as an integral constraint on the cosmic SFRD at the present time.
2.2. Star Formation Rate Density
The cosmic star formation rate density has now been measured out to z 6 (Giavalisco et al. 2004). The high-redshift points are taken from only the Lyman break galaxies, and it is unclear how severe the resulting incompleteness is since we are not sure if all star-forming galaxy populations at these redshifts are known. The plot is traditionally shown in misleading units of M Mpc-3 yr-1 versus redshift; in order to integrate-by-eye, one should plot this quantity versus time, and this has the effect of greatly increasing the apparent amount of star formation at low redshifts. Despite significant uncertainties in the SFRD at z > 3 due to incompleteness and large dust corrections, it appears that most stars in the present-day universe formed at z < 2 (see Fig. 33 of Pettini 2004).
2.3. Stellar Mass Density
The cosmic stellar mass density provides an integral constraint on the SFRD, *(t) = 0t d* / dt. See Dickinson et al. (2003) for a recent compilation, and Niv Drory's contribution to this volume for an update. Note that the stellar masses of galaxies are not direct observables but are inferred from rest-frame optical (and near-infrared) photometry by modelling each object's star formation history using an assumed initial mass function (IMF).
2.4. Cosmic Metal Enrichment History
The cosmic metal density is really a history of cosmic metal enrichment due to star formation, *(t) = 1/42 0t d* / dt (Pettini 2004). Wolfe et al. (2005, see their Fig. 7) show that the cosmic metallicity traced by DLAs rises gradually from a mean value of [M/H] = -1.5 at z 4 to a mean value of -0.7 at z 1. The range of observed DLA metallicities is somewhat higher than that of halo stars but overlaps, and is somewhat lower than that of thick disk stars and far lower than the near-solar values seen for thin disk stars in the Milky Way. The DLAs uniformly show greater metal enrichment than the Lyman forest but less than values inferred for Lyman break galaxies or quasars at the same epoch (see Figs. 8, 32 of Pettini 2004, and see Leitherer 2005 for a review). The values given above are the cosmic mean metallicity of the neutral gas traced by DLAs, but they do not represent a full census of metals, which can also be found in heavily star-forming regions that have already used up their neutral gas or can be expelled by galactic winds into the IGM, which is predominantly ionized. It is therefore useful to compare the observed DLA metallicities with those expected from the DLA star formation rates; this leads to a factor of ten deficit in the observed metallicities called the "Missing Metals Problem" (Wolfe et al. 2005, Hopkins et al. 2005, Pettini 1999). The most likely explanation is that the star-forming regions of the galaxies seen as DLAs have superwinds sufficiently strong to move most of the metals produced into the IGM.